This is a multiple linear regression where you test the individual coefficients with a t-test.
Btw, ANOVA is not involved (there are no variances that are being analyzed).
For the first coefficient, you have:
It's a t-distribution with n-3=100-3=97 degrees of freedom (generally df=n-p-1, where p is the number of parameters).
You get (slight modification of what you wrote):
Assuming an alpha of 5%, your critical t-value is t*=1,98.
(As you can see this is quite close to the 1,96 critical z-value you already had.)
Since t = -3,22 < -1,98, it follows that H0 can be rejected.
So yes, age has a significant effect on the outcome.
The method for the other coefficient is the same.